document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=79742>Question 79742</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is an extraneous solutions? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #57215 by </B><A HREF=/tutors/aboutme.mpl?userid=tutor_paul><B>tutor_paul(519)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=tutor_paul><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=tutor_paul><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=57215\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The best way to understand what extraneous roots are is to go through a problem where you get one. The following is a solution to a problem that I did previously which dealt with extraneous roots:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282y%2B7%29%2B4=y ALIGN=MIDDLE  ALT=\"sqrt%282y%2B7%29%2B4=y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "First, get the radical expression alone on one side of the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282y%2B7%29=y-4 ALIGN=MIDDLE  ALT=\"sqrt%282y%2B7%29=y-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <BR>\n" );
document.write( "Now, square both sides of the equation to get rid of the radical:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%2B7=%28y-4%29%5E2 ALIGN=MIDDLE  ALT=\"2y%2B7=%28y-4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplify the right hand side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%2B7=y%5E2-8y%2B16 ALIGN=MIDDLE  ALT=\"2y%2B7=y%5E2-8y%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Combine like terms and equate to zero:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-10y%2B9=0 ALIGN=MIDDLE  ALT=\"y%5E2-10y%2B9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Factor the expression:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-9%29%28y-1%29=0 ALIGN=MIDDLE  ALT=\"%28y-9%29%28y-1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Equate each factor to zero, and solve:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=9 ALIGN=MIDDLE  ALT=\"y=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1 ALIGN=MIDDLE  ALT=\"y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, this part is important...you need to plug these answers back in to<BR>\n" );
document.write( "the original equation to be sure they are not \"extraneous.\" An extraneous<BR>\n" );
document.write( "root may be mathematically correct, but it is not the true answer. If you<BR>\n" );
document.write( "plug y=1 back into the original equation, you will see that the equation<BR>\n" );
document.write( "DOES NOT hold true. Hence, this is an extraneous root. If you plug y=9 back<BR>\n" );
document.write( "into the original equation, you will see that the equation DOES hold true,<BR>\n" );
document.write( "so that one is your answer.\r<BR>\n" );
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document.write( "Good Luck,<BR>\n" );
document.write( "tutor_paul@yahoo.com </SPAN>\n" );
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